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Dimension splitting for quasilinear parabolic equations

Hansen, Eskil LU and Ostermann, Alexander (2010) In IMA Journal of Numerical Analysis 30(3). p.857-869
Abstract
In the current paper, we derive a rigorous convergence analysis for

a broad range of splitting schemes applied to abstract nonlinear

evolution equations, including the Lie and Peaceman-Rachford

splittings. The analysis is in particular applicable to (possibly

degenerate) quasilinear parabolic problems and their dimension

splittings. The abstract framework is based on the theory of maximal

dissipative operators, and we both give a summary of the used theory

and some extensions of the classical results. The derived

convergence results are illustrated by numerical experiments.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
degeneracy, quasilinear parabolic problems, convergence, dimension splitting
in
IMA Journal of Numerical Analysis
volume
30
issue
3
pages
857 - 869
publisher
Oxford University Press
external identifiers
  • scopus:77956017644
ISSN
0272-4979
DOI
10.1093/imanum/drn078
language
English
LU publication?
yes
id
ec81b351-ef4d-47d5-bfe0-3ffba818a541 (old id 936936)
date added to LUP
2008-01-22 19:59:33
date last changed
2018-06-03 03:12:35
@article{ec81b351-ef4d-47d5-bfe0-3ffba818a541,
  abstract     = {In the current paper, we derive a rigorous convergence analysis for<br/><br>
a broad range of splitting schemes applied to abstract nonlinear<br/><br>
evolution equations, including the Lie and Peaceman-Rachford<br/><br>
splittings. The analysis is in particular applicable to (possibly<br/><br>
degenerate) quasilinear parabolic problems and their dimension<br/><br>
splittings. The abstract framework is based on the theory of maximal<br/><br>
dissipative operators, and we both give a summary of the used theory<br/><br>
and some extensions of the classical results. The derived<br/><br>
convergence results are illustrated by numerical experiments.},
  author       = {Hansen, Eskil and Ostermann, Alexander},
  issn         = {0272-4979},
  keyword      = {degeneracy,quasilinear parabolic problems,convergence,dimension splitting},
  language     = {eng},
  number       = {3},
  pages        = {857--869},
  publisher    = {Oxford University Press},
  series       = {IMA Journal of Numerical Analysis},
  title        = {Dimension splitting for quasilinear parabolic equations},
  url          = {http://dx.doi.org/10.1093/imanum/drn078},
  volume       = {30},
  year         = {2010},
}